Hi irshad1231,
Check this example. Now please take its reference and correct your code.
HTML
<table>
    <tr>
        <td>Start date</td>
        <td><asp:TextBox ID="txtstartdate" runat="server" Text="03/01/2021"></asp:TextBox></td>
    </tr>
    <tr>
        <td>End date</td>
        <td><asp:TextBox ID="txtenddate" runat="server" Text="03/20/2021"></asp:TextBox></td>
    </tr>
    <tr>
        <td>add section</td>
        <td>
            <asp:DropDownList ID="DropDownList1" runat="server">
                <asp:ListItem Value="1">section1</asp:ListItem>
                <asp:ListItem Value="2">section2</asp:ListItem>
                <asp:ListItem Value="3">section3</asp:ListItem>
            </asp:DropDownList>
        </td>
    </tr>
    <tr>
        <td colspan="2">
            <asp:Button ID="btnSave" runat="server" Text="Add" OnClick="btnSave_Click" />
        </td>
    </tr>
</table>
<asp:GridView ID="GridView1" runat="server"></asp:GridView>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.6/jquery.min.js" type="text/javascript"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8/jquery-ui.min.js" type="text/javascript"></script>
<link href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8/themes/base/jquery-ui.css" rel="Stylesheet" type="text/css" />
<script type="text/javascript">
    $(function () {
        $("[id*=txtstartdate]").datepicker({
            showOn: 'button',
            buttonImageOnly: true,
            buttonImage: 'images/calendar.png'
        });
        $("[id*=txtenddate]").datepicker({
            showOn: 'button',
            buttonImageOnly: true,
            buttonImage: 'images/calendar.png'
        });
    });
</script>
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        GridView1.DataSource = trainerschdule();
        GridView1.DataBind();
    }
}
private DataTable trainerschdule()
{
    DataTable dt = new DataTable();
    dt.Columns.Add("EmpID");
    dt.Columns.Add("SDate");
    dt.Columns.Add("EDate");
    dt.Columns.Add("SectionID");
    dt.Rows.Add("1", "03/01/2021", "03/20/2021", "Section1");
    dt.Rows.Add("2", "03/15/2021", "04/01/2021", "Section2");
    dt.Rows.Add("3", "02/28/2021", "04/01/2021", "Section3");
    return dt;
}
protected void btnSave_Click(object sender, EventArgs e)
{
    DateTime start = Convert.ToDateTime(txtstartdate.Text.Trim());
    DateTime end = Convert.ToDateTime(txtenddate.Text.Trim());
    string section = DropDownList1.SelectedItem.Text.Trim().ToLower();
    List<DataRow> rows = (from sc in trainerschdule().AsEnumerable()
                            where sc["SectionID"].ToString().Trim().ToLower().Equals(section)
                            && (start <= Convert.ToDateTime(sc["SDate"]) && end >= Convert.ToDateTime(sc["SDate"])
                            || start <= Convert.ToDateTime(sc["EDate"]) && end >= Convert.ToDateTime(sc["EDate"]))
                            select sc).ToList();
    if (rows.Count > 0)
    {
        ClientScript.RegisterStartupScript(this.GetType(), "alert", "alert('Exist')", true);
    }
    else
    {
        ClientScript.RegisterStartupScript(this.GetType(), "alert", "alert('Not exist')", true);
        // Write code to add.
    }
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        GridView1.DataSource = trainerschdule()
        GridView1.DataBind()
    End If
End Sub
Private Function trainerschdule() As DataTable
    Dim dt As DataTable = New DataTable()
    dt.Columns.Add("EmpID")
    dt.Columns.Add("SDate")
    dt.Columns.Add("EDate")
    dt.Columns.Add("SectionID")
    dt.Rows.Add("1", "03/01/2021", "03/20/2021", "Section1")
    dt.Rows.Add("2", "03/15/2021", "04/01/2021", "Section2")
    dt.Rows.Add("3", "02/28/2021", "04/01/2021", "Section3")
    Return dt
End Function
Protected Sub btnSave_Click(ByVal sender As Object, ByVal e As EventArgs)
    Dim start As DateTime = Convert.ToDateTime(txtstartdate.Text.Trim())
    Dim end As DateTime = Convert.ToDateTime(txtenddate.Text.Trim())
    Dim section As String = DropDownList1.SelectedItem.Text.Trim().ToLower()
    Dim rows As List(Of DataRow) = (From sc In trainerschdule().AsEnumerable()
                                    Where sc("SectionID").ToString().Trim().ToLower().Equals(section) _
                                        AndAlso (start <= Convert.ToDateTime(sc("SDate")) _
                                        AndAlso [end] >= Convert.ToDateTime(sc("SDate")) _
                                        OrElse start <= Convert.ToDateTime(sc("EDate")) _
                                        AndAlso [end] >= Convert.ToDateTime(sc("EDate")))
                                    Select sc).ToList()
    If rows.Count > 0 Then
        ClientScript.RegisterStartupScript(Me.GetType(), "alert", "alert('Exist')", True)
    Else
        ClientScript.RegisterStartupScript(Me.GetType(), "alert", "alert('Not exist')", True)
        ' Write code to add.
    End If
End Sub
Screenshot
